How to make an animation so that it is smooth and plays at one speed?
One possible solution to the question (before it was updated with a use-case):

You could build curves into the corners of a trajectory path, like:



Tighter corners will result in more jumpy (sudden, unrealistic) movement.

Here I start out with a Mesh Object, then use Ctrl+Shift+B to fillet the corners, then in Edit Mode use Alt+C and convert the mesh to a Curve Object. 

Then Add a Follow Path constraint, and press Animate Path, then press Play to see what that looks like.



Sometimes It can be more convenient to see the path it will be on, rather than key-framing it.